Question: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 12}{x + 2} = \dfrac{5x + 26}{x + 2}$
Answer: Multiply both sides by $x + 2$ $ \dfrac{x^2 + 12}{x + 2} (x + 2) = \dfrac{5x + 26}{x + 2} (x + 2)$ $ x^2 + 12 = 5x + 26$ Subtract $5x + 26$ from both sides: $ x^2 + 12 - (5x + 26) = 5x + 26 - (5x + 26)$ $ x^2 + 12 - 5x - 26 = 0$ $ x^2 - 14 - 5x = 0$ Factor the expression: $ (x + 2)(x - 7) = 0$ Therefore $x = -2$ or $x = 7$ However, the original expression is undefined when $x = -2$. Therefore, the only solution is $x = 7$.